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Theoretical and Mathematical Physics

Evolution of probability measures associated with quantum systems

Grigori Gennadievich Amosov, Vladimir I. Man’ko

Published Feb 1, 2005• 1 citation
Publisher
DOI
10.1007/pl00022151

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This chapter is concerned with the application of the ontological dimension of probability to physical chance. Both ratios or proportions in populations, and dispositions and tendencies have a much longer philosophical history; their explicit association to probability and chance is, however, more of a fin de siècle development. On the frequency interpretation, probabilities are frequencies; and it is very hard to see how frequencies can explain other frequencies. While the propensity interpretation of probability overcomes the previously described difficulties for frequencies, it nonetheless has problems of its own. Collapse interpretations then postulate the second kind of openly non-deterministic evolution in order to account for the fact that measurements of any dynamical property on a quantum system routinely obtain definite results. This is the “collapse” dynamical rule: a near-instantaneous evolution of the system that takes its state to the eigenstate of the relevant operator with a certain probability.